Co Integration Springerlink

Leo Migdal

-Dec 14, 2025, 4:32 AM

The concept of co-integration posits that the linear combination of two or more nonstationary time series can be stationary if they are co-integrated (Granger 1981). Co-integration and error correction models are largely applied to solve the spurious regression problem resulting from the inclusion of nonstationary variables in a regression model. Two main approaches to modeling co-integration are single-equation residual-based and system-based analyses. One precondition for the above tests is that all variables in the co-integration regression should be integrated with the same order. When different orders of integration are identified, alternative tests such as the autoregressive distributed lag bounds test can be applied (Pesaran et al. 2001).

Since the mid-1990s, a considerable number of tourism researchers have adopted the co-integration method to address a variety of topics related to tourism demand modeling and forecasting. Numerous efforts have been undertaken to empirically... This is a preview of subscription content, log in via an institution to check access. Tax calculation will be finalised at checkout In econometrics, cointegration is a statistical property that describes a long-run equilibrium relationship among two or more time series variables, even if the individual series are non-stationary (i.e., they contain stochastic trends). In such cases, the variables may drift in the short run, but their linear combination is stationary, implying that they move together over time and remain bound by a stable equilibrium.

More formally, if several time series are individually integrated of order d (meaning they require d differences to become stationary) but a linear combination of them is integrated of a lower order, then those... That is, if (X,Y,Z) are each integrated of order d, and there exist coefficients a,b,c such that aX + bY + cZ is integrated of order less than d, then X, Y, and Z... Cointegration is a crucial concept in time series analysis, particularly when dealing with variables that exhibit trends, such as macroeconomic data. In an influential paper,[1] Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends. If two or more series are individually integrated (in the time series sense) but some linear combination of them has a lower order of integration, then the series are said to be cointegrated. A common example is where the individual series are first-order integrated (⁠ I ( 1 ) {\displaystyle I(1)} ⁠) but some (cointegrating) vector of coefficients exists to form a stationary linear combination of them.

The first to introduce and analyse the concept of spurious—or nonsense—regression was Udny Yule in 1926.[2] Before the 1980s, many economists used linear regressions on non-stationary time series data, which Nobel laureate Clive Granger... Corresponding author chengyitu@berkeley.edu Received 2019 May 19; Revised 2019 Jul 22; Accepted 2019 Aug 25; Collection date 2019 Sep 27. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Cointegration focuses on whether the long-term linear relationship between two or more time series is stationary even if this linear relationship does not exist or is not strong for the short term. Identifying the potential cointegration is important for economics, ecology, meteorology, neuroscience, and much more.

Classic methods only considered or restricted in cointegration where the order of integration of all time series is 1. We introduce a method based on searching the vector to minimize the absolute correlation of convergent cross-mapping that can explore the universal cointegration and its extent. The proposed method can be applied to time series whose order of integration is not 1, cases that are not covered by classic cointegration. The proposed method is first illustrated and validated through time series generated by mathematical models in which the underlying relationships are known and then applied to three real-world examples. Subject Areas: Global Change, Interdisciplinary Physics, Computational Mathematics This article summarizes the mathematical structure of cointegrated time series models and discusses econometric procedures commonly used to analyse cointegrated time series.

This discussion is carried out in the context of stochastic trends that follow driftless I(1) or ‘unit root’ processes. The article concludes with a brief discussion of cointegration in the context of more general stochastic trends. This chapter was originally published in The New Palgrave Dictionary of Economics, 2nd edition, 2008. Edited by Steven N. Durlauf and Lawrence E. Blume.

This is a preview of subscription content, log in via an institution to check access. Elliott, G. 1998. The robustness of cointegration methods when regressors almost have unit roots. Econometrica 66: 149–158. Elliott, G., T.J.

Rothenberg, and J.H. Stock. 1996. Efficient tests for an autoregressive unit root. Econometrica 64: 813–836.

Co Integration Springerlink

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